There has been a recent drive to find fundamental limitations of bandwidth per- formance. Such results include Rozanovs (2000) bandwidth performance of absorbers, and Gustafssons (2007) limitation for single port antennas, similar bounds on transmission coeffi- cients through a frequency selective screen and high-impedance surfaces are also known. In the present work we show a related bound for array antennas over a ground plane. We illustrate how this bound can be formulated as an array figure of merit, weighting impedance bandwidth, return loss, scan range and material and size information against each other. The derivation of the array figure of merit is based on Bode-Fano theory for a scattering passive object, and is related to the Rozanov bound of absorbers. This result is essentially a sum-rule result that only requires that the array element is scattering passive, time-invariant and linear. The bound is derived for linearly polarized periodic arrays over an infinite planar ground-plane. The array figure of merit can both be used to evaluate existing antennas. It can also be used as a prediction tool and hence as an a-priori assessment of impedance bandwidth limitations for a given antenna element. The array figure of merit contains return-loss, impedance bandwidth, scan range, and element specific information. We show how to use the array figure of merit to investigate trade-off between, e.g., return-loss and bandwidth or bandwidth versus thickness. We note that the array figure of merit easily extend to multi-band antennas.